Page 28 - Issue 39

ELITE Vol.1, Issue 39, January 2022
Vol.1, Issue 39, January

The first ever calculus textbook, appears to have been On the other hand, integral calculus studies integrals,
published in 1696 by Guillaume de l’Hôpital - i.e. finds the quantity where the rate of change is
following lectures given to him by Leibnitz- under known. While differential calculus focuses on the
the name “Analyse des Infiniment Petits pour curve itself, integral calculus concerns itself with the
l’Intelligence des Lignes Courbes”. In this textbook, space or area under the curve. Integral calculus is
he acknowledged Newton's published work of the used to figure the total size or value, such as lengths,
1680s as "nearly all about this calculus". areas and volumes.

What are the applications of differentiation that

we have been unknowingly using all throughout
What are the branches of calculus? our lives?
There are two branches of calculus, differential It might come as a surprise that we have been using
calculus and integral calculus. differentiation all our lives way before we took
Differential calculus studies derivatives, i.e. calculus in secondary school. Any mathematical
determines the rate of change of a quantity and it is formula that includes the change in a certain
the branch we are more interested in as economics variable/the change in another variable
students. (Δx/Δy) can be considered an application of
Since this branch is concerned with the study of the differentiation.
rate of change of functions with respect to their For example, in physics, we calculate the velocity of
variables, we can use it to calculate the slope of a line an object as the rate of change of its position with
or the slope of the tangent to a point on a curve. respect to a frame of reference which is a function of
Where the derivative is the slope of a line, both are time ( ̅= / ).
one and the same.

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